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Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.
If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote…
We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
Temperature is usually defined for physical systems at thermal equilibrium. Nevertheless one may wonder if it would be possible to attribute a meaningful notion of temperature to an arbitrary quantum state, beyond simply the thermal (Gibbs)…
We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength…
Qualitative Spatial and Temporal Reasoning (QSTR) is concerned with symbolic knowledge representation, typically over infinite domains. The motivations for employing QSTR techniques range from exploiting computational properties that allow…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…
The ongoing exponential rise in recording capacity calls for new approaches for analysing and interpreting neural data. Effective dimensionality has emerged as an important property of neural activity across populations of neurons, yet…
In this note we propose a definition of weak solution for an abstract Cauchy problem in a Hilbert space, and we discuss existence and uniqueness results.